I fought in the civil war on the side of the Imperium, and successfully brought it to a conclusion, defeating the Stormcloaks (that quest is finished).

I still run into Stormcloak camps periodically - for example, the Whiterun Stormcloak Camp or the Falkreath Stormcloak Camp. I can kill all the Stormcloaks, except for one named Stormcloak, who is unkillable. I can get him to crouch, panting, but after that he's unkillable and a minute or so springs up, completely healed, and resumes attacking me. An example of this kind of character is Thorygg Sun-Killer, in the Falkreath Stormcloak camp.

The Battle for Windhelm is finished and I killed Ulfric. Are these camps designed to just be eternally auto-spawning Stormcloak sites or is there something coming up plot-wise or is this some sort of bug?

It's the same on Stormcloak side. The leader of the camp is set essential and unkillable. It's not a glitch.

This is a known issues. Bethesda forgot to remove the "essential" tags off some of the NPC's in those camps., so therefore they can't die.

We'll have to wait for either a patch or the CK to fix them.... my money's riding on the CK to get to them first.

A mod will take care of this. Would like to see it be dependent as to who sits on the throne after the battle.

Imperial victory; Imperials respawn twice as quick, Stormcloaks twice slower. Stormcloak victory; other way around, of course, tho` one could leave Imperial respawn rates normal or drop down then ramp back up as they send in the reserves.